slammers:
You have a Model 37 Chiefs Special Airweight Serial range for that period was 295000 to 786544.
If the cylinder release latch is flat, then 1966 or earlier.
If the cylinder release latch is concave, then 1966 or later.
If the grips are original and have an uncheckered diamond around the grip screws, the 1968 or earlier.
If the grips are original and the checkering goes up to the grip screws, then 1968 or later.
Avoid use of PlusP or +P+ marked ammunition in this gun. I have read of cases of the aluminum frame stretching or the gun going out of time in less than 100 rounds. The general opinion is shoot standard pressure loads for practise, shoot one cylinder full of +P for familiarisation and carry it loaded with +P.
Don't use any +P+ marked ammo, as there is no industry pressure standard for this.